Suboptimality of equal lot sizes for finite-horizon problems

The paper considers the problem of determining optimal lot sizes in continuous time for finite-horizon problems with stationary parameters. Using the average cost criterion, earlier researchers concluded that the optimal lot sizes should be equal. Using the conceptually rigorous discounted cash flow analysis, it is shown that equal lot sizes are optimal only when the finite horizon is an integral multiple of the optimal reorder interval for the infinite-horizon problem or, trivially, when the discount rate is zero. In all other cases, optimal lot sizes are either monotonically increasing or decreasing. The present characterization of the optimal policy is also useful in determining optimal lot sizes.